Figure 9.1 below shows a gear drive system. Driver gear A on the shaft of the electric motor has 40 teeth that mesh with gear B with 60 teeth on a counter shaft. On the counter shaft is another driver gear C, with 30 teeth that mesh with gear D with 80 teeth on the final driven shaft. Calculate the: 9.1.1 Rotation frequency of the final driven shaft if the electrical motor rotates at 1 440 r/min 9.1.2 Velocity ratio between the input and output shafts.

NSC Mechanical Technology Fitting and Machining Transfer of movement: Figure 9.1 below shows a gear dr

Figure 9.1 below shows a gear drive system - NSC Mechanical Technology Fitting and Machining - Question 9 - 2018 - Paper 1

Question 9

Figure 9.1 below shows a gear drive system. Driver gear A on the shaft of the electric motor has 40 teeth that mesh with gear B with 60 teeth on a counter shaft. On ... show full transcript

Worked Solution & Example Answer:Figure 9.1 below shows a gear drive system - NSC Mechanical Technology Fitting and Machining - Question 9 - 2018 - Paper 1

Step 1

9.1.1 Rotation frequency of the final driven shaft if the electrical motor rotates at 1 440 r/min

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Answer

To calculate the rotation frequency of the final driven shaft, we can use the relationship between the gears. The formula is:

$N_D = \frac{N_A \times T_A \times T_C}{T_B \times T_D}$

Where:

$N_D$ = rotation frequency of the final driven shaft
$N_A$ = rotation frequency of the electrical motor = 1440 r/min
$T_A$ = number of teeth on gear A = 40
$T_B$ = number of teeth on gear B = 60
$T_C$ = number of teeth on gear C = 30
$T_D$ = number of teeth on gear D = 80

Substituting the values:

$N_D = \frac{(40 \times 30 \times 1440)}{(60 \times 80)}$

Calculating this, we find:

$N_D = 360 \, \text{r/min}$

Step 2

9.1.2 Velocity ratio between the input and output shafts

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Answer

The velocity ratio (VR) can be calculated using the formula:

$VR = \frac{N_{input}}{N_{output}}$

Here, the input speed is that of the electrical motor at $1440 \, \text{r/min}$ and the output speed is that of the final driven shaft calculated as $360 \, \text{r/min}$ .

Substituting the values:

$VR = \frac{1440}{360} = 4:1$

Figure 9.1 below shows a gear drive system - NSC Mechanical Technology Fitting and Machining - Question 9 - 2018 - Paper 1

Worked Solution & Example Answer:Figure 9.1 below shows a gear drive system - NSC Mechanical Technology Fitting and Machining - Question 9 - 2018 - Paper 1

9.1.1 Rotation frequency of the final driven shaft if the electrical motor rotates at 1 440 r/min

9.1.2 Velocity ratio between the input and output shafts

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